On the spectral instability of the Sturm-Liouville operator with a complex potential

DOI10.1134/S001226610904003XzbMath1188.47037MaRDI QIDQ731514

Kh. K. Ishkin

Publication date: 8 October 2009

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Sturm-Liouville problemspectral asymptoticsanharmonic oscillatorRegge problem

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Perturbation theory of linear operators (47A55) General theory of ordinary differential operators (47E05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (8)

On analytic perturbations of a non-self-adjoint anharmonic oscillator ⋮ Spectral properties of the nonsectorial Sturm-Liouville operator on the semiaxis ⋮ Spectral asymptotics for fourth order differential operator with two turning points ⋮ Equivalence criterion for two asymptotic formulae ⋮ Conditions of spectrum localization for operators not close to self-adjoint operators ⋮ On the class of potentials with trivial monodromy ⋮ On the localization conditions for the spectrum of a non-self-adjoint Sturm-Liouville operator with slowly growing potential ⋮ An analogue of the Gelfand-Levitan trace formula for the Sturm-Liouville operator with a meromorphic potential

Uses Software

• Eigtool

Cites Work

• Differential equations in the spectral parameter
• Semiclassical spectral instability of non-self-adjoint operators. II
• Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators
• Spectral instability for some Schrödinger operators
• A local Borg-Marchenko theorem for complex potentials
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• NON-SELF-ADJOINT DIFFERENTIAL OPERATORS
• Construction of potentials from resonance parameters
• Pseudo–spectra, the harmonic oscillator and complex resonances
• Pseudospectra of the Convection-Diffusion Operator
• Pseudospectra of Linear Operators
• Wild Spectral Behaviour of Anharmonic Oscillators
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